Linearized stability analysis of stationary solutions for surface diffusion with boundary conditions

Abstract

The linearized stability of stationary solutions to the surface diffusion flow with angle and no-flux boundary conditions is studied. In this linearized stability analysis the gradient flow structure plays a key role. As a byproduct the analysis also gives a criterion for the stability of critical points of the length functional of curves which come into contact with the outer boundary. Some examples of linearized stability are studied as well.